Questions: The function h(x)=(x+8)^4 can be expressed in the form f(g(x)) where f(x)=x^4, and g(x) is defined below: g(x)=

Solution Steps

To express the function $h(x) = (x + k)^n$ in the form $f(g(x))$, where $f(x) = x^n$, we need to define $g(x)$ such that it transforms $x$ to $x + k$.

We define $g(x) = x + 8$. This function transforms $x$ to $x + 8$, which is the necessary transformation to fit into the form of $f(g(x))$.

Applying $f(x) = x^n$ to $g(x)$, we get $f(g(x)) = (x + 8)^4$. Thus, $f(g(x)) = (x + 8)^4$, which matches the original function $h(x) = (x + 8)^4$.

Final Answer: